Question

The Outdoor Furniture Corporation manufactures two​ products, benches and picnic​ tables, for use in yards and parks. The firm has two main​ resources: its carpenters​ (labor force) and a supply of redwood for use in the furniture. During the next production​ cycle, 1 comma 400 hours of labor are available under a union agreement. The firm also has a stock of 5 comma 200 board feet of quality redwood. Each bench that Outdoor Furniture produces requires 5 ​labor-hours and 13 board feet of​ redwood; each picnic table takes 6 ​labor-hours and 26 board feet of redwood. Completed benches will yield a profit of ​$12 ​each, and tables will result in a profit of ​$18 each. How many benches and tables should Outdoor Furniture produce in order to obtain the largest possible​ profit?

Number of benches produced equals_______​(round your response to the nearest whole​ number).
Number of tables produced equals______​(round your response to the nearest whole​ number).
Optimal solution value​ = ​$_______(round your response to the nearest whole​ dollar).

Answer 1

	Bench	Picnic Table	Availability
Labor Hours	5	6	1,400 hours
Redwood (board feet)	13	26	5,200 board feet
Profit	12	18

Decision Variables: Let B and P be the number of Benches and Picnic Tables produced respectively.

Objective Function: Maximize profit.

Zmax = 12B+18P

Subject to constraints:

5T+6P <= 1400

13T+26P <= 5200

T, P >= 0

Solving the LP in solver:

Excel Model:

Solver Parameters:

Solution:

	Bench	Picnic Table
Produced Numbers	100	150

Optimal Solution Value, Maximum profit = $3900.